Question

Find the equation for the linear function that passes through the points (−5,−6) and (10,3). Answers must use whole numbers and/or fractions, not decimals.
A.Use the line tool below to plot the two points_______

B.State the slope between the points as a reduced fraction________

C.State the y-intercept of the linear function_______

D.State the linear function_________

Answer 1

Answer:

Slope: $\frac{3}{5}$

Y-intercept: -3

Equation: $y=\frac{3}{5} x-3$

Graph is attached.

Step-by-step explanation:

To find your slope using two points, use the slope formula.

$\frac{y2-y1}{x2-x1}$

Your y1 is -6, your y2 is 3.

Your x1 is -5, your x2 is 10.

$\frac{3-(-6)}{10-(-5)} \\\\\frac{9}{15} \\\\\frac{3}{5}$

Now that you have your slope, use it and one of your points in point-slope form to find your y-intercept.

$y-y1=m(x-x1)\\y-3=\frac{3}{5} (x-10)\\y-3=\frac{3}{5} x-6\\y=\frac{3}{5} x-3$

Answer 2

Answer:

A. In the graph,

Go 5 units left side from the origin in the x-axis then from that point go downward 6 unit, we will get (-5, -6),

Now, go 10 unit right from the origin in the x-axis then from that point go upward 3 unit, we will get (10, 3),

B. The slope of the line passes through (-5, -6) and (10, 3),

$m=\frac{3-(-6)}{10-(-5)}=\frac{3+6}{10+5}=\frac{9}{15}=\frac{3}{5}$

C. Since, the equation of a line passes through $(x_1, y_1)$ with slope m is,

$y-y_1=m(x-x_1)$

Thus, the equation of the line is,

$y+6=\frac{3}{5}(x+5)----(1)$

For y-intercept,

x = 0,

$y+6 = \frac{3}{5}(0+5)\implies y = 3-6=-3$

That is, y-intercept is -3.

D. From equation (1),

$5y + 30 = 3x + 15$

$\implies 3x - 5y = 15$

Which is the required linear function.