Find an equation of a line parallel to the given line and contains the given point. Write the equation in slope-intercept form.
a. line 2x+3y=2 , point (0,0)
b. line y+4=0, Point (-5,3)
2x+3y=2 has slope -2/3
So, using the point-slope form, the new line is
y-0 = -2/3 (x-0)
y = -2/3 x
y+4=0
y = -4 has slope 0
the horizontal line through (-5,3) is
y=3
a. To find an equation of a line parallel to the given line 2x + 3y = 2, we need to determine the slope of the given line.
First, let's rewrite the equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
2x + 3y = 2
Rearranging the equation, we get:
3y = -2x + 2
Divide both sides by 3:
y = (-2/3)x + 2/3
From the equation, we can see that the slope of the given line is -2/3.
Since we need to find a line parallel to this, both lines would have the same slope of -2/3.
Now, we have the slope (-2/3) and the given point (0, 0). To write the equation of the line in slope-intercept form, we can use the point-slope formula:
y - y1 = m(x - x1)
where (x1, y1) represents the given point and m represents the slope.
Plugging in the given point (0, 0) and the slope (-2/3), we have:
y - 0 = (-2/3)(x - 0)
Simplifying further, we get:
y = (-2/3)x
Therefore, the equation of the line parallel to 2x + 3y = 2 and passing through the point (0, 0) is y = (-2/3)x.
b. To find an equation of a line parallel to the given line y + 4 = 0, we need to determine the slope of the given line.
From the equation, we can see that the line is a horizontal line with a y-intercept of -4. Since it is horizontal, its slope is 0.
Since we need to find a line parallel to this, both lines would have the same slope of 0.
Now, we have the slope (0) and the given point (-5, 3). To write the equation of the line in slope-intercept form, we can use the point-slope formula:
y - y1 = m(x - x1)
where (x1, y1) represents the given point and m represents the slope.
Plugging in the given point (-5, 3) and the slope (0), we have:
y - 3 = 0(x - (-5))
Simplifying further, we get:
y - 3 = 0
Therefore, the equation of the line parallel to y + 4 = 0 and passing through the point (-5, 3) is y = 3.