Use slope-intercept form to write an equation of a line passing through the given point and having the given slope. Express the answer in standard form.
P(−4, −9); m = − 3/4
start with the point-slope form, since that is what you have.
y+9 = -3/4 (x+4)
Now just rearrange to slope-intercept or standard form.
To write an equation of a line using slope-intercept form (y = mx + b), we need the slope (m) and a point on the line (x, y).
Given:
Point: P(-4, -9)
Slope: m = -3/4
Substituting the values into the slope-intercept form, we have:
y = (-3/4)x + b
Now, we need to find the value of b, which represents the y-intercept.
To find b, substitute the coordinates of the given point (-4, -9) into the equation:
-9 = (-3/4)(-4) + b
Simplifying the equation:
-9 = 3 + b
-9 - 3 = b
b = -12
Now that we have m and b, we can substitute the values back into the slope-intercept form:
y = (-3/4)x - 12
To express the equation in standard form, we need to rearrange the terms:
4y = -3x - 48
This can also be written as:
3x + 4y = -48
Therefore, the equation of the line passing through the point (-4, -9) with a slope of -3/4 in standard form is 3x + 4y = -48.
To write an equation of a line using slope-intercept form, we need the slope (m) and a point (x,y) that the line passes through. In this case, the given slope (m) is -3/4 and the point is P(-4, -9).
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept (the point where the line crosses the y-axis).
Step 1: Substitute the given slope and point into the slope-intercept form equation.
y = (-3/4)x + b
Step 2: Solve for the y-intercept (b) by substituting the coordinates of the given point (-4, -9) into the equation.
-9 = (-3/4)(-4) + b
-9 = 3 + b
b = -9 - 3
b = -12
Step 3: Substitute the value of b into the equation.
y = (-3/4)x - 12
This is the equation of the line in slope-intercept form. To express it in standard form, we need to rearrange the equation to have the x and y terms on one side and the constant on the other side.
Multiply every term by 4 to eliminate the fraction:
4y = -3x - 48
Rearrange the equation to have the constant on the right side:
3x + 4y = -48
This is the equation of the line in standard form.