Y-Intercept OverviewDefinition:The y-intercept is the point where a graph crosses the y-axis. In other words, it is the value of y when \(x=0\). Show
Y-Intercept Sample Questions and FAQs How to find the y-intercept:There is more than one way to find the y-intercept, depending on your starting information. Below are three ways to identify the y-intercept on a graph, in a table, or with an equation:
First, identify the slope and a point on the graph. Once this is done, write a linear equation in slope-intercept form (y = mx + b). Using the given point (x, y) and the slope m, rewrite the equation by substituting the appropriate values for x, y, and m. Given this information, solve the equation for b to identify the y-intercept. Example: Consider a graph containing the point (-2, 5) where the slope is 3.
Using a table or a graph, identify two points shown. First, record the coordinates (x, y) for each point. Using this information, find the rise and run to identify the slope. Calculate the rise by finding the difference in the y-coordinates of the two points. Calculate the run by finding the difference in the x-coordinates of these two points. Divide the difference in y-coordinates by the difference in x-coordinates to find the slope. Once the slope has been identified, write a linear equation in slope-intercept form (y = mx + b). Using one set of coordinates (x, y) and the slope m, rewrite the equation by substituting the appropriate values for x, y, and m. Then, solve the equation for b to identify the y-intercept. Y-intercept Example Consider a graph containing the points (3, 6) and (-1, -2). Find the y-intercept.
If you already have the equation of the line, solve algebraically to find the y-intercept. Since the y-intercept always has a corresponding x-value of 0, replace x with 0 in the equation and solve. Example: Find the y-intercept of the line \(3x+(-2y)=12\)
Finding the y-intercept in a quadratic functionIn a quadratic function, the y-intercept is the point at which the parabola crosses the y-axis. In the graph shown, the y-intercept is -3. The standard form of a quadratic equation is written as \(y=ax^2+bx+c\), where x and y are variables and a, b, and c are known constants. To find the y-intercept from a quadratic equation, substitute 0 as the value for x and solve. The y-intercept is always equal to the value of c in the equation. Example: Find the y-intercept in the quadratic equation \(y=2x^2+3x+4\).
FAQsPractice Frequently Asked QuestionsQHow do you find the \(y\)-intercept?AThere is more than one way to find the \(y\)-intercept, depending on your starting information. If the linear equation is given, solve algebraically to find the \(y\)-intercept. Since the \(y\)-intercept always has a corresponding \(x\)-value of \(0\), replace \(x\) with \(0\) in the equation and solve for \(y\). On a graph, the \(y\)-intercept can be found by finding the value of \(y\) when \(x=0\). This is the point at which the graph crosses through the \(y\)-axis. QWhat is the \(y\)-intercept of an equation?AWhen the equation of a line is written in slope-intercept form \((y=mx+b)\), the \(y\)-intercept is the constant, which is represented by the variable \(b\). For example, in the linear equation \(y=4x-5\), the \(y\)-intercept is \(-5\). QWhere is the \(y\)-intercept on a graph?AThe \(y\)-intercept is the point where the graph of a line crosses the
\(y\)-axis. In the coordinate plane shown, the \(y\)-intercept is \(4\) because the graph passes through \(4\) on the \(y\)-axis. QWhy is the \(y\)-intercept important?AThe \(y\)-intercept is important because it tells the value of \(y\) when \(x=0\). It provides a starting point for a linear function. QHow do I find slope and \(y\)-intercept?AOn a graph, the \(y\)-intercept is the point where the line intersects the \(y\)-axis. The corresponding \(x\)-coordinate is always \(0\). The slope is found by calculating rise over run. This is done by finding the difference in the \(y\)-coordinates and \(x\)-coordinates and dividing these differences. When a linear equation is written in slope-intercept form \((y=mx+b)\), the slope is represented by the variable \(m\). It is the coefficient to \(x\) in the equation. The \(y\)-intercept is the constant, represented by the variable \(b\). QIs \(b\) the \(y\)-intercept?AWhen a linear equation is written in slope-intercept form \((y=mx+b)\), the \(y\)-intercept is represented by the constant variable \(b\). For example, in the equation \(y=6x+8\), the variable \(b\) corresponds with \(8\). This is the \(y\)-intercept. QWhat does the \(y\)-intercept mean in real life?AThe \(y\)-intercept is the \(y\)-value that corresponds to \(x\) when \(x=0\). In real life, this often refers to the starting point when something is being measured. For instance, consider population change in the United States. In this scenario, the \(x\)-values could represent time, measured in years. The \(y\)-values could represent the population, measured in millions of people. When \(x=0\), this value represents the starting year for measuring population change. The corresponding \(y\)-value represents the size of the population in the starting year. This value is the \(y\)-intercept. Practice QuestionsQuestion #1: y-intercept = 3 y-intercept = 2 y-intercept = 4 y-intercept = \(\frac{1}{2}\) Show Answer Answer: The correct answer is A. The y-intercept is the point where the graph crosses the y-axis. When studying the graph above, notice that the line crosses the y-axis at (0, 3), so 3 is the y-intercept. Hide Answer Question #2: y = ax2 + bx + c Show Answer Answer: The correct answer is C. In a quadratic equation, the variable c represents the y-intercept. This is the point where the graph intersects the y-axis. Hide Answer Question #3: \(-\frac{1}{2}\) 2 4 \(\frac{1}{2}\) Show Answer
Answer: The correct answer is D. When a function is in slope-intercept form, the y -intercept can quickly be identified because it is represented by the variable b. In this example, b is \(\frac{1}{2}\), therefore the y-intercept is \(\frac{1}{2}\). Hide Answer Question #4: y-intercept = 0 y-intercept = 1 y-intercept = 0.25 y-intercept = -1.5 Show Answer Answer: The correct answer is B. The y-intercept is the point where the graph crosses the y-axis. When studying the graph above, notice that the line crosses the y-axis at 1, so 1 is the y-intercept. Hide Answer Question #5: \(y=2x^2-5x+3\) \(y=2x^2-3x+4\) \(y=2x^2-4x+7\) \(y=2x^2-6x+8\) Show Answer Answer: The correct answer is B. The quadratic equation \(y=2x^2-3x+4\) is written in standard form. This makes it easier to identify the y-intercept, because c always represents the y-intercept. The graph shows a quadratic equation that intersects the y-axis at 4, and the only equation where c is equal to 4 is Choice B. Hide Answer How do you find the yThe standard form of a quadratic equation is written as y=ax2+bx+c, where x and y are variables and a, b, and c are known constants. To find the y-intercept from a quadratic equation, substitute 0 as the value for x and solve. The y-intercept is always equal to the value of c in the equation.
How do you find the yThe equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept. In our equation, y = โ 7 x + 4 , we see that the y-intercept of the line is 4.
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