The equation of line whose slope is 3/4 and y-intercept is 6 is 3x - 4y = -6.
A slope of line is the change in y coordinate with respect to the change in x coordinate.
As we know the slope intercept form of the line is given by
y = mx + b
Where,
m is the slope of the line
and b is the y intercept.
The y-intercept of a graph is the point where the graph intersects the y-axis.
According to the given question
We have different equation of lines
3x - 4y = -6 ....(i)
3x -4y = 6 ....(ii)
3x -4y = -24 ...(iii)
The slope intercept form of equation (i) is given by
3x - 4y = -6
⇒ -4y = -6 - 3x
⇒ y = -6/-4 -3x/4
⇒[tex]y =\frac{3}{2} -\frac{3}{4}x[/tex]
Hence, the slope of the line 3x - 4y = -6 is -3/4
For y intercept put x = 0 in , y = 3/2 -3/4x
⇒ y = 3/2
Therefore the y intercept of line 3x - 4y = -6 is 3/2.
The Slope intercept form of equation (ii) is given by
3x - 4y = 6
⇒ -4y = 6 - 3x
⇒ [tex]y = \frac{6}{-4} -\frac{3}{-4}x[/tex]
⇒ [tex]y = \frac{-3}{2} + \frac{3}{4}x[/tex]
Hence, the slope of the line 3x - 4y = 6 is 3/4
For y intercept put x = 0 in y = -3/2 + 3/4x.
⇒ y = -3/2
Therefore, y intercept for 3x - 4y = 6 is -3/2.
The slope intercept form of equation (iii) is given by
3x - 4y = -24
⇒ -4y = -24 - 3x
⇒ [tex]y = \frac{-24}{-4} -\frac{3}{-4}x[/tex]
⇒ [tex]y = 6+ \frac{3}{4} x[/tex]
Hence, the slope of the line 3x - 4y = -24 is 3/4.
For the y intercept put x = 0 in y = 6 + 3/4x.
⇒ y = 6
Therefore, y intercept for 3x - 4y = -24 is 6.
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