Question

In slope intercept form y = mx + b
in standard form ax + by = c

The slope is 5 passing through ( -1, 4).
The line passes through point ( 3, -4) and (-2, 2)
The slope is and the y-intercept is (0,4)
The x intercept -3 and the y-intercept is 6
5. Passing through the points (-1, -2) and (5, 3)
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Answer 1

Answer:

The slope is 5 passing through ( -1, 4).

The line passes through point ( 3, -4) and (-2, 2)

The slope is and the y-intercept is (0,4)

The x intercept -3 and the y-intercept is 6

5. Passing through the points (-1, -2) and (5, 3)

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Answer 2

Answer:

The equation of the lines are $y=5x+9$

Step-by-step explanation:

1) The line which has slope 5 has the equation of the form $y=5x+c$.

In order to find the y intercept $c$, substitute the point (-1,4) in the equation.

We get

$4=5(-1)+c\\4=-5+c\\c=5+4=9$

Hence the equation of the line in slope intercept form is $y=5x+9$ and equation in standard form is $y-5x=9$

2) Given the line is passing through the points (3,-4) and (-2,2). So the slope of the line is

$m=\frac{2-(-4)}{-2-3}=\frac{6}{-5}=\frac{-6}{5}$

So the equation of the line has the form $y=\frac{-6}{5}x+c$

To find the value of $c$, substitute on of the points in the equation.

$2=\frac{-6}{5}\times (-2)+c\\2=\frac{12}{5} +c\\c=2-\frac{12}{5}=\frac{10-12}{5}=\frac{-2}{5}$

Hence the equation of the line in slope intercept form is $y=\frac{-6}{5}x-\frac{2}{5}$ and equation in standard form is $5y+6x=-2$

3) Only y-intercept is given the equation will be of the form $y=mx+4$, where $m$ is the slope of the line.

4) Given that the x-intercept is -3 and y-intercept is 6. So (-3,0) and (0,6) are points on the line. Thus the slope is given by

$m=\frac{6-0}{0-(-3)}=\frac{6}{3}=2$

Hence the equation of the line in slope intercept form is $y=2x+6$ and equation in standard form is $y-2x=6$

5) Given the line is passing through the points (-1,-2) and (5,3). So the slope of the line is

$m=\frac{3-(-2)}{5-(-1)}=\frac{5}{6}$

So the equation of the line has the form $y=\frac{5}{6}x+c$

To find the value of $c$, substitute on of the points in the equation.

$3=\frac{5}{6}\times (5)+c\\3=\frac{25}{6} +c\\c=3-\frac{25}{6}=\frac{18-25}{6}=\frac{-7}{6}$

Hence the equation of the line in slope intercept form is $y=\frac{5}{6}x-\frac{7}{6}$ and equation in standard form is $6y-5x=-7$