Question

Write the equation of the

Answer 1

Answer:

$y = \frac{1}{5} x+3$  

Step-by-step explanation:

From the given information, we already know two points the line intersects. It states that the line has a y-intercept of 3. The y-intercept is the point at which the line intersects the y-axis. Thus, the line also intersects (0,3). (Remember that all points on the y-axis have an x-value of 0.) Now we have enough information to write an equation.  

1) Find the slope of the line with the slope formula, $m = \frac{y_2-y_1}{x_2-x_1}$. Substitute the x and y values of (-5,2) and (0,3) into the formula and solve:

$m = \frac{(3)-(2)}{(0)-(-5)} \\m = \frac{3-2}{0+5}\\m = \frac{1}{5}$

So, the slope of the line is $\frac{1}{5}$.

2) Now we can write the equation in slope-intercept form, represented by the formula $y = mx + b$. Substitute values for $m$ and $b$ in the formula.

The $m$ represents the slope, so substitute $\frac{1}{5}$ for it. The $b$ represents the y-intercept, so substitute $3$ for it. This gives the following answer and equation in slope-intercept form:  

$y = \frac{1}{5} x+3$