Answer:
Gradient: -4
y-intercept: [tex]-\frac{9}{2}[/tex]
Step-by-step explanation:
Step 1 - Subtract 8x from both sides to isolate the 2y + 9
[tex]8x + 2y + 9 = 0\\8x + 2y + 9 - 8x = 0 - 8x\\2y + 9 = -8x\\[/tex]
Step 2 - Subtract 9 from both sides to isolate the 2y:
[tex]2y + 9 = -8x\\2y + 9 - 9 = -8x - 9\\2y = -8x - 9[/tex]
Step 3 - Divide both sides of the equation by 2:
[tex]\frac{2y}{2} = \frac{-8x}{2} - \frac{9}{2}\\y = -4x - \frac{9}{2}[/tex]
In this form, y = mx + b, the m value is the gradient with the b value being the y-intercept. This means:
[tex]y = -4x - \frac{9}{2}\\\\m = -4\\b = -\frac{9}{2} \\\\[/tex]
Resulting in the gradient being -4 and the y-intercept being [tex]-\frac{9}{2}[/tex].
Hope this helps!
