Question

Write the equation of a line that has a slope of 3 and passes through the point (5, 7).

Answer 1

Answer:

y = 3x - 8    

Step-by-step explanation:

All the options are written in slope-intercept ( $y = mx + b$) form. So, what we can do with the given information is write the equation in point-slope form first, then convert it to slope-intercept form.  

1) First, use the point-slope formula $y-y_1 = m (x-x_1)$ to find the point-slope equation of the line. Substitute $m$, $x_1$, and $y_1$ for real values.

Since $m$ represents the slope, substitute 3 in its place. Since $x_1$ and $y_1$ represent the x and y values of one point the line intersects, substitute the x and y values of (5,7) into the appropriate places in the formula as well. This gives the following equation of the line in point-slope form:  

$y-7 = 3(x-5)$

2) Now, isolate y in the above equation to find its slope-intercept form.

$y-7=3(x-5)\\y-7 = 3x-15\\y = 3x -8$

Thus, the answer would be the third option as it matches the result we received.