Can you please show me the steps and solution to this problem?
I really don't understand. Thank you very much.
Write an equation in slope-intercept form of the line through points S(-2, -7) and T(4, 3).
you have two points. The slope is 10/6 = 5/3. Now, using he point-slope form, you have
y-3 = (5/3)(x-4)
y = 5/3 x - 20/3 + 3
y = 5/3 x - 11/3
Or, solving for
y = mx+b
3 = 4m+b
-7 = -2m+b
and solve for m and b.
Thank you Steve so much!
To write the equation of a line in slope-intercept form (y = mx + b), you need to determine the slope (m) and the y-intercept (b).
Step 1: Calculate the slope (m).
The slope can be found using the formula:
m = (y2 - y1) / (x2 - x1)
In this case, the coordinates of point S are (-2, -7) and the coordinates of point T are (4, 3). Substituting these values into the slope formula, we get:
m = (3 - (-7)) / (4 - (-2))
m = (3 + 7) / (4 + 2)
m = 10 / 6
m = 5/3
So, the slope (m) is 5/3.
Step 2: Determine the y-intercept (b).
To find the y-intercept, you can substitute the coordinates of one of the given points (S or T) and the slope (m) into the slope-intercept form (y = mx + b), and solve for b.
Let's choose point S(-2, -7) to substitute into the equation:
-7 = (5/3)(-2) + b
-7 = -10/3 + b
To solve for b, add 10/3 to both sides:
-7 + 10/3 = b - 10/3 + 10/3
-21/3 + 10/3 = b
-11/3 = b
So, the y-intercept (b) is -11/3.
Step 3: Write the equation in slope-intercept form.
Now that you have the slope (m = 5/3) and the y-intercept (b = -11/3), you can write the equation of the line in slope-intercept form:
y = (5/3)x - 11/3
Therefore, the equation in slope-intercept form of the line through points S(-2, -7) and T(4, 3) is y = (5/3)x - 11/3.