(a) Complete the statements below about y=4x and y=x (b) y=x-7/2 and y=x

Question

(a) Complete the statements below about y= 4x and y=x

Compared to the graph of y = x, the graph of y= 4x is... (Steeper, Equally Steep, Less Steep)

Compared to the graph of y = x, the graph of y = 4x intersects the y-axis at... (A higher point, the same point, a lower point)

(b) Complete the statements below about y= x - 7/2 and y=x

Compared to the graph of y = x, the graph of y=x -7/2 is... (Steeper, Equally Steep, Less Steep)

Compared to the graph of y = x, the graph of y= x -7/2 intersects the y-axis at... (A higher point, the same point, a lower point)

Answer 1

y=x goes through the origin of a coordinate grid and has a slope of 1. If a slope of 4 is multiplied by x then the slope will be steeper because slope is rise/run where rise is the y axis and run is the x axis and since 4 is a whole number which is can also be in this form 4/1 it means that the slope will go up 4 and right 1 which is steeper than up 1 and right 1. This can be clearly be demonstrated if this equation were drawn a coordinate grid. s for the y-intercept the original equation y=x had no y-intercept since it crossed the origin and because y=4x is just a change in the slope the y-intercept remains the same.

The second part has the equation y=x-7/2 which has a negative y-intercept that is negative 6 and a half in the negative y-axis from the origin. Since this question also asks for the slope due to asking about steepness. Since this equation has a y-intercept included while y=x which has a slope of 1 this kind of equation does not show any change in the slope unlike the previous equation so the answer is equally steep. as for the last part of this second question there clearly is a change in the y-intercept to this equation when compared toy=x since as mentioned before this linear equation has a y-intercept oof -7/2 which is 6 and a half since -7/6 equals -3 and 1/2 down the y-axis from the origin so there a change to the y-intercept a result.