Final answer:
To find the Standard Form of the equation of a line with a slope of 4 passing through the point (5, −2), you start with the slope-intercept form, plug in the given slope and point to find the y-intercept, and then rearrange the terms to get the Standard Form, which is −4x + y = −22.
Step-by-step explanation:
The question is asking how to find the equation of a line in Standard Form when given a slope and a point that the line passes through. The slope of the line is given as 4, and the line passes through the point (5, −2). To find the equation of the line in Standard Form, which is Ax + By = C, where A, B, and C are integers, we can follow these steps:
- Start with the slope-intercept form of the line equation, y = mx + b, where m is the slope and b is the y-intercept.
- Insert the given slope and the point into the equation to solve for b.
- Using the value of b, write the equation of the line with the given slope.
- Finally, rearrange the equation into Standard Form by moving all terms to one side of the equation.
For this particular problem, the steps would look like this:
- Begin with the slope-intercept form: y = 4x + b.
- Insert the point (5, −2) into the equation to find b: −2 = 4(5) + b. Solve for b to get b = −2 - 20 = −22.
- Write the line equation with the found y-intercept: y = 4x - 22.
- Rearrange to Standard Form: 4x - y = 22, and if we require A to be positive, we can multiply by −1 to get −4x + y = −22 as the final Standard Form equation.