how to find the x and y intercept using this table (-10,-28) (-6,-21) (-2,-14)

Question

how to find the x and y intercept using this table (-10,-28) (-6,-21) (-2,-14)

Answer 1

This question is asking us to find the x-intercept and y-intercept of a line that passes through three points.

Step 0: Clarify the Question

This question is lacking a little bit of information, so I am going to make an assumption. I assume that we are trying to find the x-intercept and y-intercept of the line defined by those points. Otherwise, there would be no x or y intercept.

Step 1: Find the Slope

To find the equation of the line, we will first need the slope of the line. We can find this by using the general slope formula for two points.

m = (y₂ - y₁) / (x₂ - x₁)

The 'y' variables are the y coordinates, the 'x' variables are x coordinates, and the 1 and 2 are the names of the points. Let's define what the points are. It is important to know that it does not matter which points we use for point #1 or point #2, as long as we are consistent with it. Let's define (-6,-21) as point #1 and (-2,-14) as point #2.

x₁ = -6, y₁ = -21, x₂ = -2, and y₂ = -14

Now we can calculate the slope 'm'.

m = (y₂ - y₁) / (x₂ - x₁)

m = (-14 - -21) / (-2 - -6)

m = (-14 + 21) / (-2 + 6)

m = 7 / 4

Step 2: Define the Line

To get the equation of the line, we will need the point-slope equation of a line.

y - y₁ = m(x - x₁)

Let's substitute the 'm', 'x₁', and 'y₁' into the equation.

y - y₁ = m(x - x₁)

y - -21 = (7/4)(x - -6)

y + 21 = (7/4)(x + 6)

y + 21 = (7/4)x + (42/4)

y = (7/4)x + (21/2) - 21

y = (7/4)x - (21/2)

Step 3: Finding the x-Intercept

Now that we have an equation for the line, we can finally find the intercepts. Since x-intercepts lie on the x-axis, their y value is equal to zero. This means we can find x-intercepts by setting y equal to zero and solving for x.

y = (7/4)x - (21/2)

y = 0

0 = (7/4)x - (21/2)

21/2 = (7/4)x

21/2 * 4/7 = x

x = 6

Step 4: Finding the y-Intercept

Similarly, since y-intercepts lie on the y-axis, their x value is equal to zero. This means we can find y-intercepts by setting x equal to zero and solving for y.

y = (7/4)x - (21/2)

x = 0

y = (7/4)(0) - (21/2)

y = -21/2

Therefore, the line defined by those points has an x-intercept of (6, 0) and a y-intercept of (0, -21/2).