Question 3: Draw the following straight-line graphs using the gradient - int ercept method: a. \( y+4=2 x \) b. \( h(x)=\frac{3}{2} x+3 \) c. \( 2 y=-6 x+10 \)

To graph the equation \( y + 4 = 2x \), you can first rearrange it to get \( y = 2x - 4 \). Here, the gradient (slope) is 2, meaning for every 1 unit you move right on the x-axis, you move up 2 units on the y-axis. The y-intercept is -4, so plot the point (0, -4) and use the slope to find another point, like (1, -2). For the equation \( h(x) = \frac{3}{2}x + 3 \), the gradient is \(\frac{3}{2}\), indicating you move up 3 units for every 2 units you move to the right. The y-intercept is 3, so start by marking (0, 3) on your graph. From there, for each 2 units along the x-axis, draw a point 3 units higher until you connect the dots for your line. In the equation \( 2y = -6x + 10 \), simplify it to get \( y = -3x + 5 \). Here, the gradient is -3, so each unit you move right, you move down 3 units. The y-intercept is 5, so plot (0, 5) first. Then, for each 1 unit to the right, go 3 units down, plotting points and connecting them to form your line!