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Quiz 10
1.) What is the slope of the line $y=4$?
Solution: The slope is $0$ because it is a horizontal line. (Could consider 2 solutions, say $(0,4)$ and $(1,4)$ and compute the slope directly.)
2.) What is the slope of the line $y=\dfrac{3}{2}x+7$?
Solution: Recall that the equation of a line is said to be in "slope-intecept form" if it is written in the form $y=mx+b$ for some numbers $m$ and $b$. When writing a line in this way, the number $m$ is the slope and the number $b$ is the $y$-coordinate of the $y$-intercept (so the $y$-intercept is the point $(0,b)$). This given line is given in slope-intercept form, so we see that the slope is $m=\dfrac{3}{2}$.
3.) What is the slope of the line $3x+4y=9$?
Solution: This equation is not in slope-intercept form. However we can put it into slope intercept form by solving for $y$. To do this, first subtract $3x$ to get
$$4y=9-3x,$$
and then divide both sides by $4$ to get
$$y=\dfrac{9-3x}{4} = \dfrac{9}{4} - \dfrac{3}{4}x = -\dfrac{3}{4}x + \dfrac{9}{4}.$$
From this we observe that the slope is $m=-\dfrac{3}{4}$.
4.) What is the $y$-intercept of the line $y=2x+3$?
Solution: This line is in slope-intercept form, so we may immediately say that the $y$-intercept is $\left(0,3\right)$.
5.) What is the $y$-intercept of the line $2y=5x+4$?
Solution: This equation is not in slope-intercept form, so we will put it into that form by solving for $y$. To do that, divide both sides by $2$ to get
$$y = \dfrac{5x+4}{2} = \dfrac{5}{2}x+\dfrac{4}{2} = \dfrac{5}{2}x + 2.$$
From this we see that the $y$-intercept is $(0,2)$.
