Question

I only need 12 and 17, first good response i will give brainliest please i’m desperate

Answer 1

Answer:

$\textsf{12.} \quad y = 6x - 5$

$\textsf{17.} \quad y=-\dfrac{1}{4}x-2$

Step-by-step explanation:

Question 12

Find the slope of the line by substituting two points from the given table into the slope formula.

Define the points:

• Let (x₁, y₁) = (2, 7)
• Let (x₂, y₂) = (3, 13)

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{13-7}{3-2}=\dfrac{6}{1}=6$

Substitute the found slope and point (2, 7) into the point-slope formula to create an equation of the line:

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

$\implies y-7=6(x-2)$

$\implies y-7=6x-12$

$\implies y=6x-5$

Question 17

Given:

• f(4) = 3
• f(0) = -2

Therefore, two points on the line are:

• (4, -3)
• (0, -2)

The y-intercept is the y-value when x = 0.

Therefore, the y-intercept of the line is -2.

$\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\ y=mx+b \\\\where:\\ \phantom{ww} \bullet m is the slope. \\ \phantom{ww} \bullet b is the y -intercept.\\\end{minipage}}$

Substitute the y-intercept and the point (4, 3) into the slope-intercept formula and solve for m to find the slope:

$\implies y=mx+b$

$\implies -3=m(4)-2$

$\implies -1=4m$

$\implies m=-\dfrac{1}{4}$

Therefore, the equation of the line is:

$y=-\dfrac{1}{4}x-2$