A line passes through the point (1,7) and has a slope of -8 . Write an equation for this line

Answer 1

Question: A line passes through the point (1,7) and has a slope of -8 . Write an equation for this line.

Answer:

Step 1: Coordinates are written as (x, y). That means for the coordinate (1, 7), 1 is the x and 7 is the y.

Step 2: Plug in the values into y=mx+b and solve for b.

We know y is 7, x is 1, and m (the slope) is -8.

So, 7= -8(1)+b

7=-8+b

+8 +8

---------------------

15=b

Step 3: Write the equation in y=mx+b form replacing the m and b for -8 and 15.

y=-8x+15

Answer 2

In order to answer this question, we must use Slope-Intercept Form and fill in the missing variables. Slope-intercept form is as follows:

y = mx + b, where m = the slope of the line and b = the y-intercept of the line.

In this case, the slope is given (slope = -8), so we know that m = -8 in this case. Now, we can use the definition of a slope to find out what the y-intercept is. The definition of a slope is as follows:

y₂ - y₁

---------------- = slope

x₂ - x₁

What this means is that we must find 2 different points on the line, find the difference between their y-values (or change in y), then divide that number by the difference in their x-values (or change in x).

The problem gives us one coordinate (1,7), and we must find the other one using the definition of a y-intercept. The y-intercept is any point in a line where the x-value = 0. So, given this information, we can create the point (0, b) where b = the y-intercept, and plug those values into the definition of a slope to find the value of b:

7 - b 7 - b

--------- = -8, ------- = -8, 7 - b = -8, -b = -15, b = 15

1 - 0. 1

Therefore, m = -8 and b = 15.

We can plug this into the slope-intercept form and get our final answer:

y = -8x + 15

Let me know if you have any questions regarding this explanation.