Let's solve the given question step-by-step:
We are given the equation of a line in slope-intercept form, which is [tex]\( y = -4x + 7 \)[/tex].
1. Identify the slope ([tex]\( m \)[/tex]) and the y-intercept ([tex]\( b \)[/tex]) from the equation:
- The slope ([tex]\( m \)[/tex]) is the coefficient of [tex]\( x \)[/tex], which is [tex]\(-4\)[/tex].
- The y-intercept ([tex]\( b \)[/tex]) is the constant term, which is [tex]\( 7 \)[/tex].
2. To graph the line, we start by plotting the y-intercept.
- The y-intercept is the point where the line crosses the y-axis. For [tex]\( y = -4x + 7 \)[/tex], this point is [tex]\((0, 7)\)[/tex].
3. Next, use the slope to find another point on the line.
- The slope [tex]\(-4\)[/tex] means that for every 1 unit increase in [tex]\( x \)[/tex], [tex]\( y \)[/tex] decreases by 4 units.
- Starting from the y-intercept [tex]\((0, 7)\)[/tex], if we increase [tex]\( x \)[/tex] by 1, then [tex]\( y \)[/tex] will decrease by 4 units:
- When [tex]\( x = 1 \)[/tex], [tex]\( y = -4(1) + 7 = -4 + 7 = 3 \)[/tex].
- This gives us another point [tex]\((1, 3)\)[/tex].
4. Plot the points [tex]\((0, 7)\)[/tex] and [tex]\((1, 3)\)[/tex] on the graph.
5. Draw a straight line through these points to complete the graph of the line.
The resulting line will have a downward slope due to the negative slope value of [tex]\(-4\)[/tex], and it will intersect the y-axis at [tex]\(7\)[/tex].
So, the graph of [tex]\( y = -4x + 7 \)[/tex] is a straight line that goes through the points [tex]\((0, 7)\)[/tex] and [tex]\((1, 3)\)[/tex] with a slope of [tex]\(-4\)[/tex].
