Answer:
[tex]y = \frac{1}{5} x+3[/tex]
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, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of (-5,2) and (0,3) into the formula and solve:
[tex]m = \frac{(3)-(2)}{(0)-(-5)} \\m = \frac{3-2}{0+5}\\m = \frac{1}{5}[/tex]
So, the slope of the line is [tex]\frac{1}{5}[/tex].
2) Now we can write the equation in slope-intercept form, represented by the formula [tex]y = mx + b[/tex]. Substitute values for [tex]m[/tex] and [tex]b[/tex] in the formula.
The [tex]m[/tex] represents the slope, so substitute [tex]\frac{1}{5}[/tex] for it. The [tex]b[/tex] represents the y-intercept, so substitute [tex]3\\[/tex] for it. This gives the following answer and equation in slope-intercept form:
[tex]y = \frac{1}{5} x+3[/tex]
