Question

What is an equation of the line that passes through the points (0,7) and (5,4? Put your answer in fully reduced form.

Answer 1

Answer (assuming it can be in slope-intercept format):

$y = -\frac{3}{5} x+7$  

Step-by-step explanation:

When knowing the y-intercept of a line and its slope, we can write an equation representing it in slope-intercept form, or $y = mx + b$.

1) First, find the slope of the equation. Use the slope formula, $m = \frac{y_2-y_1}{x_2-x_1}$, to find the slope. Substitute the x and y values of the given points into the formula and simplify:

$m = \frac{(4)-(7)}{(5)-(0)} \\m = \frac{4-7}{5-0} \\m = \frac{-3}{5}$

Thus, the slope is $-\frac{3}{5}$.

2) Usually, we would have to use one of the given points and the slope to put the equation in point-slope form. However, notice that the point (0,7) has an x-value of 0. All points on the y-axis have an x-value of 0, thus (0,7) must be the y-intercept of the line. Now that we know the slope of the line and its y-intercept, we can already write the equation in slope-intercept format, represented by the equation  $y = mx + b$. Substitute $m$ and $b$ for real values.

Since $m$ represents the slope, substitute $-\frac{3}{5}$  in its place in the equation. Since $b$ represents the y-intercept, substitute 7 in its place. This gives the following equation and answer:

$y = -\frac{3}{5} x+7$