Question

creating linear equations
equations & inequalities

1. which equation represents a line with a slope of -1 that passes through (0, 4)?

a. $y = -x + 4$
b. $y = -x - 4$
c. $y = 4x - 1$
d. $y = 4x + 1$

1. these ordered pairs define a function: ${(1, 1), (2, \frac{1}{4}), (3, -7)}$

select all ordered pairs that are in the inverse of the function.
a. (1,1) b. $(\frac{1}{4}, 2)$ c. $(-7, 3)$ d. (2, 4)
e. $(3, -\frac{1}{7})$ f. $(2, -\frac{1}{4})$ g. (3, 7)

1. which equation represents a line passing through the point (8, 9) with a slope of 3?

a. $y = 3x - 15$
b. $y = 3x - 8$
c. $y = 3x + 33$
d. $y = 3x + 9$

1. determine the slope, $m$, and $y$-intercept, $b$, of a line that passes through the points (-2, 6) and (4, -3).

$m = \text{ⓐ } -4.5 \text{ ⓑ } -1.5 \text{ ⓒ } 0.5$
$b = \text{ⓐ } -9 \text{ ⓑ } 3 \text{ ⓒ } 7$

1. select all the equations that represent a line passing through the point (-2, 5) with a slope of 4.

a. $y - 5 = 4(x + 2)$ b. $y + 5 = 4(x - 2)$ c. $y + 2 = 4(x - 5)$
d. $4x - y = -13$ e. $4x - y = 13$ f. $2x - 5y = 4$

1. write the equation of the line represented by $y = \frac{2}{3}x - 5$ in standard form.

Explanation:

Question 1

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Substitute slope and y - intercept

We know that the slope $m=- 1$ and the line passes through $(0,4)$. When $x = 0$, $y=b$, so $b = 4$. Substituting $m=-1$ and $b = 4$ into $y=mx + b$, we get $y=-x + 4$.

Step1: Recall inverse function definition

If a function has an ordered pair $(a,b)$, then the inverse function has the ordered pair $(b,a)$.

Step2: Find inverse pairs

For the function $\{(1,1),(2,\frac{1}{4}),(3, - 7)\}$, the inverse function will have pairs:

• For $(1,1)$, the inverse pair is $(1,1)$ (since $a = b=1$)
• For $(2,\frac{1}{4})$, the inverse pair is $(\frac{1}{4},2)$
• For $(3,-7)$, the inverse pair is $(-7,3)$

Step1: Recall point - slope form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope.

Step2: Substitute values

We have $m = 3$, $x_1=8$, $y_1 = 9$. Substituting into the point - slope form:
$y-9=3(x - 8)$

Step3: Simplify the equation

$y-9=3x-24$
$y=3x-24 + 9$
$y=3x-15$

Answer:

a. $y=-x + 4$

Question 2