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il63 [147K]
3 years ago
8

A line that passes through the point (–1, 3) has a slope of 2. Find another point on the line

Mathematics
2 answers:
bezimeni [28]3 years ago
6 0
Y-y1=m(x-x1)
for slope=m
a point =(x1,y1)

slope=2
point= (-1,3)
y-3=2(x+1)
y-3=2x+2
y=2x+5
test given points

A.
(1,5)
5=2(1)+5
5=7
false

B.
(1,4)
4=2(1)+5
4=7
false

C.
(-3,2)
2=2(-3)+5
2=-6+5
2=-1
false

D.
(0,5)
5=2(0)+5
5=0+5
5=5
true

answer is D
Harman [31]3 years ago
6 0
The answer would be D. If you graphed this line, you would find that one of the y intercept matches choice D. You can also put this into the slope-intercept equation which is y= 2x +5. So if you plug in the point (0,5), it will look like this: 
5=2(0)+5. The 2 will be 0 so it ends up being 5=5 which is true for this line.


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to get the equation of any straight line, we simply need two points off of it, let's use those two points in the picture below.

(\stackrel{x_1}{0}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}}\implies \cfrac{3}{1}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_2=m(x-x_2) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_2}{5}=\stackrel{m}{3}(x-\stackrel{x_2}{1})

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