please help me with this problem? I don't know how ro do it. please show me step by step.
Write the slope intercept form the equations of the lines through the given point parallel to the given line and (B) perpendicular to given line.
point slope
((7,-2) m= 1/2
Let me change the problem. Find a line perpenduclar to a line thrue 4,5 and having slope 4
new slope of perpendicular line..-1/4
y=mx + b
5=(-1/4)4 + b
b=6
y=(-1/4)x+ 6 is the equation.
thanks now i get it
Lowest terms
4x+12/5x^2 + 21x + 18
To write the slope-intercept form of the equations of lines through a given point parallel and perpendicular to a given line, follow these steps:
Step 1: Understand the slope-intercept form
The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept (the point where the line intersects the y-axis).
Step 2: Find the equation of the line parallel to the given line
Since the line you are trying to find is parallel to the given line, it means they will have the same slope (m). In this case, the given slope is m = 1/2.
Using the point-slope form of a linear equation (y - y1 = m(x - x1)), substitute in the values of the given point (7,-2) and the slope (1/2) to get the equation.
(y - (-2)) = (1/2)(x - 7)
Simplifying the equation gives:
y + 2 = (1/2)(x - 7)
Step 3: Write the equation in slope-intercept form
To convert the equation to slope-intercept form, we isolate y on one side:
y + 2 = (1/2)x - 7/2
Simplifying and rearranging, we get:
y = (1/2)x - 7/2 - 2
y = (1/2)x - 7/2 - 4/2
y = (1/2)x - 11/2
Therefore, the equation of the line through the point (7,-2) parallel to the given line is y = (1/2)x - 11/2.
Step 4: Find the equation of the line perpendicular to the given line
To find the equation of the line perpendicular to the given line, we need to determine the negative reciprocal of the slope of the given line. In this case, the slope (m) of the given line is 1/2.
The negative reciprocal of 1/2 is -2/1 or -2.
Using the point-slope form again, substitute in the values of the given point (7,-2) and the negative reciprocal of the slope (-2).
(y - (-2)) = (-2)(x - 7)
Simplifying the equation gives:
y + 2 = -2(x - 7)
Step 5: Write the equation in slope-intercept form
To convert the equation to slope-intercept form, isolate y on one side:
y + 2 = -2x + 14
Simplifying and rearranging, we get:
y = -2x + 14 - 2
y = -2x + 12
Therefore, the equation of the line through the point (7,-2) perpendicular to the given line is y = -2x + 12.