Question

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

O y = 3x + 8
O y = 5x + 7
O y = 3x - 8
O y = 7x + 5

Answer 1

y = 3x - 8

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.