All ACT Math Resources
Example Question #1 : How To Find The Equation Of A Curve
Find the slope of the following line: 6x – 4y = 10
Putting the equation in y = mx + b form we obtain y = 1.5x – 2.5.
The slope is 1.5.
Example Question #2 : How To Find The Equation Of A Curve
What is the x-intercept of the line in the standard coordinate plane for the following equation?
This question is asking us to find the x-intercept. Remember that the y-value is equal to zero at the x-intercept. Substitute zero in for the y-variable in the equation and solve for the x-variable.
Add 2 to both sides of the equation.
Divide both sides of the equation by 6.
The line crosses the x-axis at 2.
Example Question #3 : How To Find The Equation Of A Curve
What is the equation of a line that has an x-intercept of 4 and a y-intercept of -6?
The equation of a line can be written in the following form:
In this formula, m is the slope, and b represents the y-intercept. The problem provides the y-intercept; therefore, we know the following information:
We can calculate the slope of the line, because if any two points on the function are known, then the slope can be calculated. Generically, the slope of a line is defined as the function's rise over run, or more technically, the changes in the y-values over the changes in the x-values. It is formally written as the following equation:
The problem provides the two intercepts of the line, which can be written as and . Substitute these points into the equation for slope and solve:
Substitute the calculated values into the general equation of a line to get the correct answer: