Write the equation of the line, with the given properties, in slope-intercept form.
slope = -4, through (-6, 5)
The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
We are given the slope m = -4 and a point on the line (-6, 5). We can use the point-slope form of the equation of a line to find the equation in slope-intercept form.
y - y1 = m(x - x1) (point-slope form)
Substituting the values, we get:
y - 5 = -4(x - (-6))
y - 5 = -4(x + 6)
y - 5 = -4x - 24
y = -4x - 19
Therefore, the equation of the line in slope-intercept form is y = -4x - 19.
Actually the answer by the bot is correct
To write the equation of a line in slope-intercept form (y = mx + b), we need to know the slope (m) and a point on the line (x, y). In this case, the given slope is -4, and the line passes through the point (-6, 5).
Step 1: Substitute the values of the slope and the coordinates of the point into the equation.
So, plugging in -4 for m, -6 for x, and 5 for y, we have:
y = -4x + b
Step 2: Solve for the y-intercept (b) using the given point (-6, 5).
Since the line passes through the point (-6, 5), we can substitute these values into the equation and solve for b.
5 = -4(-6) + b
Simplifying, we get:
5 = 24 + b
Step 3: Solve for b
Subtracting 24 from both sides, we have:
5 - 24 = b
-19 = b
Step 4: Write the final equation
Now that we have the value of b, we can substitute it back into the equation:
y = -4x - 19
Therefore, the equation of the line in slope-intercept form is y = -4x - 19.
y = mx + b
5 = (-6)(-4) + b
5 = 24 + b
-19 = b
Our y-intercept is 19. Now, our equation is:
y = 6-x + (-19)
Not sure if my answer is correct. can someone check my solution?