Answer
$y = -2x + 4$
Work Step by Step
We know that the x-intercept is the point on a line where it crosses the x-axis; it is also the value of $x$ when $y = 0$. For this line, the x-intercept is $2$.
The y-intercept is the point on a line where it crosses the y-axis; it is also the value of $y$ when $x = 0$. For this line, the y-intercept is $4$.
Given this information, we already have two points on our line: the x-intercept coordinate $(2, 0)$ and the y-intercept coordinate$(0, 4)$. We can use these two points to find the slope of the line first.
Let's use the formula to find the slope $m$ given two points:
$m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.
Let's plug in these values into this formula:
$m = \frac{4 - 0}{0 - 2}$
Subtract the numerator and denominator to simplify:
$m = \frac{4}{-2}$
Divide the numerator and denominator by their greatest common denominator, which is $2$:
$m = -2$
Now that we have the slope, we can use one of the points and plug these values into the point-slope equation, which is given by the formula:
$y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point on the line.
Let's plug in the points and slope into the formula:
$y - 0 = -2(x - 2)$
We can get rid of the $0$:
$y = -2(x - 2)$
Use the distributive property on the right side of the equation to rewrite this equation in slope-intercept form:
$y = -2x + 4$
This equation is now in slope-intercept form.
