What is the equation of the line that passes through the point left bracket, 3, comma, 5, right bracket(3,5) and has a slope of 22?
The equation of the line that passes through the point (3,5) and has a slope of 22 can be found using the point-slope form.
Point-slope form: y - y1 = m(x - x1)
Where (x1, y1) is the given point, and m is the slope.
Using the given point (3,5) and the slope 22:
y - 5 = 22(x - 3)
Now, we can simplify this equation:
y - 5 = 22x - 66
y = 22x - 61
Therefore, the equation of the line is y = 22x - 61.
To find the equation of a line, we need to use the slope-intercept form, which is given by:
y = mx + b
where m is the slope of the line, and b is the y-intercept.
We are given that the slope is 22, so we can substitute this value into the equation:
y = 22x + b
To find the value of b, we need to use the coordinates of the given point (3,5) and substitute them into the equation.
We have the point (x, y) = (3,5):
5 = 22(3) + b
Now we can solve for b:
5 = 66 + b
Subtract 66 from both sides:
5 - 66 = b
b = -61
Now that we have the value of b, we can substitute it back into the equation:
y = 22x - 61
Therefore, the equation of the line passing through the point (3,5) with a slope of 22 is y = 22x - 61.
To find the equation of a line given a point and a slope, you can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
where (x1, y1) represents the given point, and m represents the slope.
In this case, the given point is (3, 5) and the slope is 22. Plugging these values into the equation, we have:
y - 5 = 22(x - 3)
Now, let's simplify the equation:
y - 5 = 22x - 66
Next, we can rewrite the equation in slope-intercept form, which is y = mx + b, where b represents the y-intercept. To do this, we isolate y by adding 5 to both sides of the equation:
y = 22x - 66 + 5
Simplifying further:
y = 22x - 61
Therefore, the equation of the line that passes through the point (3, 5) with a slope of 22 is y = 22x - 61.