To describe the appearance of the graph of the equation [tex]\( y = -9x + 4 \)[/tex], let's analyze its components and properties step by step.
1. Form of the Equation: The given equation is [tex]\( y = -9x + 4 \)[/tex], which is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
2. Slope [tex]\( m \)[/tex]:
- In the equation [tex]\( y = -9x + 4 \)[/tex], the slope [tex]\( m \)[/tex] is [tex]\(-9\)[/tex].
- A negative slope (like [tex]\(-9\)[/tex]) means that the line will decline as it moves from left to right across the graph.
3. Y-Intercept [tex]\( b \)[/tex]:
- The y-intercept [tex]\( b \)[/tex] is [tex]\( 4 \)[/tex]. This means that the line crosses the y-axis at the point [tex]\( (0, 4) \)[/tex].
4. Graph Description:
- Because the slope is [tex]\(-9\)[/tex], the line will be steep and will slope downward.
- Starting at the y-intercept (0, 4), as [tex]\( x \)[/tex] increases, [tex]\( y \)[/tex] will decrease rapidly.
Given this analysis, the graph of the equation [tex]\( y = -9x + 4 \)[/tex] is:
- A line that slopes down.
Thus, the graph of [tex]\( y = -9x + 4 \)[/tex] is a line that slopes downwards.
