Question

Use the graph (point one is (0,-3), point two is (1,1).) to derive the equation of the line in slope-intercept form.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To derive the equation of the line in slope-intercept form, we need to first find the slope of the line using the two given points.

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:

m = (y2 - y1) / (x2 - x1).

Given point one is (0,-3) and point two is (1,1), we can substitute the coordinates into the formula:

m = (1 - (-3)) / (1 - 0)
m = (1 + 3) / 1
m = 4.

Now that we found the slope, we can use the slope-intercept form of the equation of a line, y = mx + b, where m is the slope and b is the y-intercept.

Since the line passes through point one (0, -3), we can substitute the x and y coordinates into the equation to solve for b:

-3 = 4(0) + b
-3 = 0 + b
b = -3.

Now that we found the y-intercept, we can write the equation of the line in slope-intercept form as:

y = 4x - 3.

Answer 2

what about (0,-2) (1,1)

Answer 3

[AI-generated answer — Bot GPT 3.5]

Given the two points (0, -2) and (1, 1), we can find the equation of the line in slope-intercept form using the same method as before.

First, let's find the slope:

m = (1 - (-2)) / (1 - 0)
m = (1 + 2) / 1
m = 3.

Now that we found the slope, we can use the slope-intercept form of the equation of a line, y = mx + b, where m is the slope and b is the y-intercept.

Since the line passes through point one (0, -2), we can substitute the x and y coordinates into the equation to solve for b:

-2 = 3(0) + b
-2 = 0 + b
b = -2.

Now that we found the y-intercept, we can write the equation of the line in slope-intercept form as:

y = 3x - 2.

Answer 4

write y - 3x = 7 in slope-intercept form.

Answer 5

[AI-generated answer — Bot GPT 3.5]

To write the equation \( y - 3x = 7 \) in slope-intercept form, we need to solve for y by isolating it on one side of the equation.

Starting with \( y - 3x = 7 \), let's add 3x to both sides:

\( y - 3x + 3x = 7 + 3x \)

This simplifies to:

\( y = 3x + 7 \)

The equation is now in slope-intercept form, with the slope being 3 and the y-intercept being 7.

Answer 6

Graph the equation x - y = 4 using the form y = mx + b

Answer 7

[AI-generated answer — Bot GPT 3.5]

To graph the equation \(x - y = 4\) using the slope-intercept form \(y = mx + b\), we need to solve the equation for y. Starting with the given equation:

\[ x - y = 4 \]

Subtract x from both sides:

\[ -y = -x + 4 \]

Divide by -1 to make the coefficient of y positive:

\[ y = x - 4 \]

Now, compare this equation with the slope-intercept form \(y = mx + b\). We can see that the slope \(m\) is 1 and the y-intercept \(b\) is -4.

Therefore, the equation is in the form \(y = x - 4\).

This means the slope is 1, and the y-intercept is -4. This means that the line goes through the point (0,-4) and has a slope of 1, meaning it rises 1 unit for every 1 unit it moves to the right.

To graph it, you can plot the y-intercept at (0, -4) and then use the slope to determine a second point on the line. You can then draw a line through both points.