Question

which equation graphs a line that passes through the point $(-7,5)$ and has a slope of zero?
$y = -7$
$y = 5$
$x = -7$
$x = 5$
question 9
two students graphed a line using a slope of $-4$ and the point $(-2,5)$.

• starting at $(-2, 5)$, asher moved down 4 units and right 1 unit to plot the second point.
• bella also started at $(-2, 5)$ and moved up 4 units and right 1 unit to plot the second point.

who plotted the first two points of the line correctly? how do you know?
bella; a slope always goes upward and to the right
asher; a slope always goes downward and to the right
asher; a negative slope means move down and then to the right
bella; a negative slope means move up and then to the right

Explanation:

First Question

Step1: Recall zero-slope line form

A line with slope 0 is horizontal, with equation $y = k$ (where $k$ is a constant, the y-coordinate of all points on the line).

Step2: Match the point's y-value

The line passes through $(-7,5)$, so the y-coordinate is 5. Substitute $k=5$ into the line equation.

Slope is defined as $\frac{\text{rise}}{\text{run}}$. A slope of $-4$ means $\frac{\text{rise}}{\text{run}} = \frac{-4}{1}$, so for a run of +1 (right 1 unit), the rise is -4 (down 4 units). Asher followed this rule, while Bella used a positive rise which does not match the negative slope.

Answer:

$y=5$

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Second Question