a) The equation of the straight line shown above is y = 4x.
b) 'y = 3x + 5 passes through (0, 5)'
c) A straight line has the same gradient as y = 3x + 5 and it passes through the point (0, 12), the equation of this straight line is y= 3x + 12.
In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
- m represents the slope or rate of change.
- x and y are the points.
- c represents the y-intercept or initial value.
Part a.
Based on the information provided about this equation, we have the following slope and y-intercept;
Slope, m = 2.
y-intercept, c = 0.
By substituting the given parameters, we have the following:
y = mx + c
y = 4x + 0
y = 4x
Part b.
Since this straight line has equation y = 3x + 5, its graph must pass through the point (0, 5) because that is its y-intercept.
Part c.
Since the straight line has the same gradient as y = 3x + 5 and it passes through the point (0, 12), the equation of this straight line is given by;
y = mx + c
y= 3x + 12.