Question

1) Find an equation of the line that passes through the point and has the indicated slope m. (Let x be the independent variable and y be the dependent variable.) (1, 8); m = -1/2
2) Find an equation of the line that passes through the points. (2, 4) and (3, 7)

3) Find an equation of the line that has slope m and y-intercept b. (Let x be the independent variable and y be the dependent variable.) m = −2; b = −1

4) Write the equation in the slope-intercept form.y − 7 = 0 _____________ Then find the slope of the corresponding line _______ then find the y-intrcept of the corresponding line (x,y)= ( ______ )

Answer 1

Answer:

1) The equation of a line is  $y=-\frac{1}{2}x+\frac{17}{2}$.

2) The equation of the line that passes through the points (2,4) and (3,7) is $y=3x-2$

3) The equation of the line that has slope m = −2 and y-intercept equal to -1 is $y=-2x-1$

4) The slope-intercept form of $y-7=0$ is $y=7$, where the slope is zero and the y-intercept is (0, 7).

Step-by-step explanation:

1) The equation of a line with slope m, passing through the point $(x_1,y_1)$, is

$y-y_1=m(x-x_1)$

We know that $m = -\frac{1}{2}$ and the point is (1,8). Therefore, the equation of the line is

$y-8=-\frac{1}{2} (x-1)\\\\y-8+8=-\frac{1}{2}\left(x-1\right)+8\\\\y=-\frac{1}{2}x+\frac{1}{2}+8\\\\y=-\frac{1}{2}x+\frac{17}{2}$

2) The equation of a line is typically written as

$y=mx+b$

where m is the slope and b is the y-intercept.

The slope of a line is a measure of how fast the line "goes up" or "goes down" and is given by

$m=\frac{y_2-y_1}{x_2-x_1}$

To find the equation of the line that passes through the points (2, 4) and (3, 7), the first step is to find the slope.

Applying the definition of the slope, we get that

$m=\frac{7-4}{3-2}=3$

Now, we find the y-intercept with the help of point (2, 4) and the general form of the equation of a line

$4=3(2)+b\\b=-2$

The equation of the line that passes through the points (2,4) and (3,7) is $y=3x-2$

3) The equation of the line that has slope m = −2 and y-intercept equal to -1 is

$y=-2x-1$

4) The slope-intercept form of $y-7=0$ is $y=7$, where the slope is zero and the y-intercept is (0, 7).